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Physica Scripta

Entanglement and causality in the interaction of the two-level atom with the field

Evgeniy O. Kiktenko, Sergey M. Korotaev

Published Oct 23, 2013• 5 citations
Publisher

Abstract

The interaction between an initially pure two-level atom and the mixed thermal quantized field mode in the framework of the Jaynes?Cummings model is considered with the employment of quantum causal analysis . At the high temperature of the field, a distinction between the resulting properties of initially excited and ground atom states smoothes over and the whole state turns out to be causally asymmetric, entangled and ?classical? in the entropic sense. The average asymptotic entanglement is found. It is revealed that the thermalization acting on the field corresponds to the stronger causality and entanglement decay, rather than the thermalization acting only on the atom.

DOI
10.1088/0031-8949/88/05/055008

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The interaction between an initially pure two-level atom and the mixed thermal quantized field mode in the framework of the Jaynes?Cummings model is considered with the employment of quantum causal analysis . At the high temperature of the field, a distinction between the resulting properties of initially excited and ground atom states smoothes over and the whole state turns out to be causally asymmetric, entangled and ?classical? in the entropic sense. The average asymptotic entanglement is found. It is revealed that the thermalization acting on the field corresponds to the stronger causality and entanglement decay, rather than the thermalization acting only on the atom.
The Jaynes-Cummings model (JCM) of a two-level atom interacting with a quantized radiation field has been investigated theoretically. Of particular interest is the transition of a quantized electromagnetic field of the model to a classical one in the limit of very large average photon number. In this thesis, two aspects of the JCM are examined. Firstly, it is shown that, in contrast to the general case, for specic initial atom-field states, there is exact correspondence between the atomic inversion predicted by the JCM and that predicted by the semiclassical model in which the field is treated classically from the outset. Secondly, the degree of quantum entanglement of the JCM is investigated quantitatively and it is shown that, at any nite absolute temperature greater than zero, the atom and field are never separable and the degree of quantum entanglement approaches zero in the high and low temperature limits
The Jaynes-Cummings model of a single two-level atom interacting with a quantized single-mode coherent field generates at the half-revival time a dynamically disentangled atom-field state. At such times, the field is in asymptotically pure Schrödinger cat state, a macroscopic superposition of distinct field eigenmodes. In this paper we address the problem of field purity when a second atom is allowed to interact with the cavity mode and becomes entangled with the first atom via their mutual cavity field with which they interact. We employ the collective Dicke states to describe the cooperative effects on the entanglement and show that the second atom spoils the purity of the field state except for special cases of the atom-field coupling or of initial conditions.
The effects of a chaotic field on the entanglement dynamics in a system of interaction of a two-level atom with a single-mode cavity field prepared in a Glauber–Lachs state were investigated in the framework of the Jaynes–Cummings model. We found that the entanglement is a non-monotonic function of the ratio of the mean numbers of thermal photons and coherent photons or, equivalently, the degree of initial mixedness of the system. There is an optimal value of this ratio up to which thermal photons contribute increasingly to the entanglement and after which they weaken the strength of the entanglement.
In this paper, we have investigated the entanglement dynamics between two initially entangled qubits interacting with two independent thermal cavities modes in the framework of resonant double Jaynes-Cummings model. We obtain the exact solution for the model under consideration and derive the time dependence of the atom-atom negativity. Results reveal that for entangled atoms the initial atomic quantum correlations can partially restore its original values for a finite interval of time, even for relatively high cavity temperatures.
How mixed can one component of a bi-partite system be initially and still become entangled through interaction with a thermalized partner? We address this question here. In particular, we consider the question of how mixed a two-level system and a field mode may be such that free entanglement arises in the course of the time evolution according to a Jaynes-Cummings type interaction. We investigate the situation for which the two-level system is initially in a mixed state taken from a one-parameter set, whereas the field has been prepared in an arbitrary thermal state. Depending on the particular choice for the initial state and the initial temperature of the quantized field mode, three cases can be distinguished: (i) free entanglement will be created immediately, (ii) free entanglement will be generated, but only at a later time different from zero, (iii) the partial transpose of the joint state remains positive at all times. It will be demonstrated that increasing the initial temperature of the field mode may cause the joint state to become distillable during the time evolution, in contrast to a non-distillable state at lower initial temperatures. We further assess the generated entanglement quantitatively, by evaluating the logarithmic negativity numerically, and by providing an analytical upper bound.
How mixed can one component of a bi-partite system be initially and still become entangled through interaction with a thermalized partner? We address this question here. In particular, we consider the question of how mixed a two-level system and a field mode may be such that free entanglement arises in the course of the time evolution according to a Jaynes-Cummings type interaction. We investigate the situation for which the two-level system is initially in a mixed state taken from a one-parameter set, whereas the field has been prepared in an arbitrary thermal state. Depending on the particular choice for the initial state and the initial temperature of the quantized field mode, three cases can be distinguished: (i) free entanglement will be created immediately, (ii) free entanglement will be generated, but only at a later time different from zero, (iii) the partial transpose of the joint state remains positive at all times. It will be demonstrated that increasing the initial temperature of the field mode may cause the joint state to become distillable during the time evolution, in contrast to a non-distillable state at lower initial temperatures. We further assess the generated entanglement quantitatively, by evaluating the logarithmic negativity numerically, and by providing an analytical upper bound.